We can combine Theorem REF  applied to a polynomial matrix \(P(\lambda )\)  and the equality of the number of the minimal indices of \(L(\lambda )\)  and \(P(\lambda )\)  with [1]} for proving that any minimal linear polynomial system matrix of a polynomial matrix \(P(\lambda )\)  is always a GLR-linearization of \(P(\lambda )\). The reverse result is not true in general. Observe also that any minimal polynomial system matrix of a polynomial matrix \(P(\lambda )\)  must have the block \(A(\lambda )\)  in (REF ) unimodular, because \(P(\lambda )\)  does not have finite poles.
